23. Bunker Hill Monument at this time, October 13, is about 64 feet high; supposing a stone weighing 4 tons, should fall from its top to the earth, what would be its force, or momentum ? Ans. 578440 lbs. That is, it would strike the earth with more force, than the weight of two hundred and fifty tons.

SECTION LXIX.

MECHANICAL POWERS.

THAT body which communicates motion to another, is called the power.

The body which receives motion from another, is called the weight.

The mechanical powers are five, the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Screw and the Wedge.

LEVER.

The lever is a bar, movable about a fixed point, called its fulcrum or prop. It is in theory considered as an inflexible line, without weight. It is of three kinds; the first, when

the prop is between the weight and the power; the second, when the weight is between the prop and the power; the third, when the power is between the prop and the weight.

A power and weight acting upon the arms of a lever, will balance each other, when the distance of the point, at which power is applied to the lever from the prop, is to the distance of the point at which the weight is applied, as the weight is to the power.

Therefore, to find what weight may be raised by a given power, we adopt the following

RULE. As the distance between the body to be raised, or balanced, and the fulcrum or prop, is to the distance between the prop and the point, where the power is applied; so is the power to the weight which it will balance.

1. If a man weighing 170 pounds be resting upon a lever 10 feet long, what weight will he balance on the other end, supposAns. 1530 lbs. ing the prop one foot from the weight?

2 If a weight of 1530 pounds were to be raised by a lever 10 feet long, and the prop fixed one foot from the weight, what power applied to the other end of the lever would balance it? Ans. 170 lbs.

3. If a weight of 1530 pounds be placed one foot from the prop, at what distance from the prop must a power of 170 pounds be applied to balance it?

Ans. 9 feet.

4. At what distance from a weight of 1530 pounds must a prop be placed, so that as a power of 170 pounds, applied 9 feet from Ans. 1 foot. the prop, may balance it?

5. Supposing the earth to contain 4.000.000.000.000.000.000.000 cubic feet, and each foot to weigh 100 pounds, and that the earth was suspended at one end of a lever, its centre being 6000 miles from the fulcrum or prop; and that a man was able, at the other end of the lever, to pull, or press with a force of 200 pounds; what must be the distance between the man and the fulcrum, that he might be able to move the earth?

Ans. 12.000.000.000.000.000.000.000.000 miles.

6. Supposing the man in the last question to be able to move his end of the lever 100 feet per second, how long would it take him to raise the earth one inch?

Ans. 52.813.479.690 years, 17 days, 14 hours, 57 min. 463 sec.

To find, therefore, how large a power must be applied to the wheel to raise a given weight on the axis, we adopt the following

RULE. As the diameter of the wheel is to the diameter of the axle, so is the weight to be raised by the axle, to the power that must be applied to the wheel.

7. If the diameter of the axle be 6 inches, and the diameter of the wheel 4 feet, what power must be applied to the wheel to raise 960 pounds at the axle ? Ans. 120 lbs. 8. If the diameter of the axle be 6 inches, and the diameter of the wheel 4 feet, what power must be applied to the axle to raise 120 pounds at the wheel?

Ans. 960 lbs. 9. If the diameter of the axle be 6 inches, and 120 pounds applied to the wheel, raise 960 pounds at the axle, what is the diameter of the wheel?

Ans. 4 feet. 10. If the diameter of the wheel be 4 feet, and 120 pounds applied to the wheel, raise 960 pounds at the axle, what is the diameter of the axle ?

Ans. 6 inches.

PULLEY.

The pulley is a small wheel, movable about its axis by means of a cord, which passes over it.

When the axis of a pulley is fixed, the pulley only changes the direction of the power; if movable pulleys are used, an equilibrium is produced, when the power is to the weight, as one to the number of ropes applied to them. If each movable pulley has its own rope, each pulley will be double the pow

er.

To find the weight, that may be raised by a given power. RULE. Multiply the power by twice the number of movable pulleys, and the product is the weight.

11. What power must be applied to a rope, that passes over one movable pulley, to balance a weight of 400 pounds?

Ans. 200 lbs

12. What weight will be balanced by a power of 10 pounds, attached to a cord that passes over 3 movable pulleys?

Ans. 60 lbs. 13. What weight will be balanced by a power of 144 pounds, attached to a cord, that passes over 2 movable pulleys ?

Ans. 576 lbs.

14. If a cord, that passes over two movable pulleys be attached to an axle 6 inches in diameter; and if the wheel be 60 inches in diameter, what weight may be raised by the pulley, by applyAns. 5760 lbs. ing 144 pounds to the wheel?

INCLINED PLANE.

An inclined plane is a plane, which makes an acute angle with the horizon.

The motion of a body, descending down an inclined plane, is uniformly accelerated.

The force with which a body descends, by the force of attraction, down an inclined plane, is to that, with which it would descend freely, as the elevation of the plane to its length; or, as the size of its angle of inclination to radius.

To find the power, that will draw a weight up an inclined plane.

RULE. Multiply the weight by the perpendicular height of the plane, and divide this product by the length.

15. An inclined plane is 50 feet in length, and 10 feet in perpendicular height; what power is sufficient to draw up a weight of 1000 pounds? Ans. 200 lbs.

16. What weight applied to a cord passing over a single pulley at the elevated part of an inclined plane, will be able to sustain a weight of 1728 pounds, provided the plane was 600 feet long, and its perpendicular height 5 feet? Ans. 143 lbs.

17. A certain railroad, one mile in length, has a perpendicular elevation of 50 feet; what power is sufficient to draw a train of cars weighing 20000 pounds, up this elevation ?

Ans. 189 lbs.

THE SCREW.

The screw is a cylinder, which has either a prominent part, or a hollow line passing round it in a spiral form, so inserted in one of the opposite kind, that it may be raised or depressed at pleasure, with the weight upon its upper, or suspended beneath its lower surface.

In the screw, the equilibrium will be produced, when the power is to the weight, as the distance between the two contiguous threads, in a direction parallel to the axis of the screw, to the circumference of the circle described by the power in one revolution.

To find the power that should be applied to raise a given weight.

RULE. As the distance between the threads of the screw is to the circumference of the circle described by the power, so is power to the weight to be raised.

the

NOTE. One third of the power is lost in overcoming friction.

18. If the threads of a screw be 1 inch apart, and a power of 100 pounds be applied to the end of a lever 10 feet long, what force will be exerted at the end of the screw?

Ans. 75398.20+ lbs. 19. If the threads of a screw be an inch apart, what power must be applied to the end of a lever 100 inches in length to raise 100000 pounds? Ans. 79.5774+lbs.

20. If the threads of a screw be an inch apart, and a power of 79.5774+pounds be applied to the end of a lever 100 inches in length, what will be raised?

Ans. 100.000 lbs.

21. If a power of 79.5774+ pounds be applied to the end of a lever 100 inches long; and if by this force a weight of 100.000 pounds be raised, what was the distance of the threads of the screw? Ans. an inch.

22. If a power of 79.5774+ pounds be applied to the end of a lever; and if by this force a weight of 100.000 pounds be raised, what must be the length of the lever, if the threads of the screw bean inch apart? Ans. 100 inches.